TSTP Solution File: SEU120+1 by SInE---0.4

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SInE---0.4
% Problem  : SEU120+1 : TPTP v5.0.0. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : Source/sine.py -e eprover -t %d %s

% Computer : art05.cs.miami.edu
% Model    : i686 i686
% CPU      : Intel(R) Pentium(R) 4 CPU 2.80GHz @ 2793MHz
% Memory   : 2018MB
% OS       : Linux 2.6.26.8-57.fc8
% CPULimit : 300s
% DateTime : Sun Dec 26 04:42:31 EST 2010

% Result   : Theorem 0.17s
% Output   : CNFRefutation 0.17s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   15
%            Number of leaves      :    3
% Syntax   : Number of formulae    :   31 (   6 unt;   0 def)
%            Number of atoms       :   88 (  22 equ)
%            Maximal formula atoms :    8 (   2 avg)
%            Number of connectives :  104 (  47   ~;  28   |;  26   &)
%                                         (   3 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   4 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   4 con; 0-2 aty)
%            Number of variables   :   51 (   2 sgn  32   !;  11   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(6,axiom,
    ! [X1,X2] :
      ( disjoint(X1,X2)
    <=> set_intersection2(X1,X2) = empty_set ),
    file('/tmp/tmpPjPwM1/sel_SEU120+1.p_1',d7_xboole_0) ).

fof(10,axiom,
    ! [X1] :
      ( X1 = empty_set
    <=> ! [X2] : ~ in(X2,X1) ),
    file('/tmp/tmpPjPwM1/sel_SEU120+1.p_1',d1_xboole_0) ).

fof(11,conjecture,
    ! [X1,X2] :
      ( ~ ( ~ disjoint(X1,X2)
          & ! [X3] : ~ in(X3,set_intersection2(X1,X2)) )
      & ~ ( ? [X3] : in(X3,set_intersection2(X1,X2))
          & disjoint(X1,X2) ) ),
    file('/tmp/tmpPjPwM1/sel_SEU120+1.p_1',t4_xboole_0) ).

fof(13,negated_conjecture,
    ~ ! [X1,X2] :
        ( ~ ( ~ disjoint(X1,X2)
            & ! [X3] : ~ in(X3,set_intersection2(X1,X2)) )
        & ~ ( ? [X3] : in(X3,set_intersection2(X1,X2))
            & disjoint(X1,X2) ) ),
    inference(assume_negation,[status(cth)],[11]) ).

fof(16,plain,
    ! [X1] :
      ( X1 = empty_set
    <=> ! [X2] : ~ in(X2,X1) ),
    inference(fof_simplification,[status(thm)],[10,theory(equality)]) ).

fof(17,negated_conjecture,
    ~ ! [X1,X2] :
        ( ~ ( ~ disjoint(X1,X2)
            & ! [X3] : ~ in(X3,set_intersection2(X1,X2)) )
        & ~ ( ? [X3] : in(X3,set_intersection2(X1,X2))
            & disjoint(X1,X2) ) ),
    inference(fof_simplification,[status(thm)],[13,theory(equality)]) ).

fof(27,plain,
    ! [X1,X2] :
      ( ( ~ disjoint(X1,X2)
        | set_intersection2(X1,X2) = empty_set )
      & ( set_intersection2(X1,X2) != empty_set
        | disjoint(X1,X2) ) ),
    inference(fof_nnf,[status(thm)],[6]) ).

fof(28,plain,
    ! [X3,X4] :
      ( ( ~ disjoint(X3,X4)
        | set_intersection2(X3,X4) = empty_set )
      & ( set_intersection2(X3,X4) != empty_set
        | disjoint(X3,X4) ) ),
    inference(variable_rename,[status(thm)],[27]) ).

cnf(29,plain,
    ( disjoint(X1,X2)
    | set_intersection2(X1,X2) != empty_set ),
    inference(split_conjunct,[status(thm)],[28]) ).

cnf(30,plain,
    ( set_intersection2(X1,X2) = empty_set
    | ~ disjoint(X1,X2) ),
    inference(split_conjunct,[status(thm)],[28]) ).

fof(40,plain,
    ! [X1] :
      ( ( X1 != empty_set
        | ! [X2] : ~ in(X2,X1) )
      & ( ? [X2] : in(X2,X1)
        | X1 = empty_set ) ),
    inference(fof_nnf,[status(thm)],[16]) ).

fof(41,plain,
    ! [X3] :
      ( ( X3 != empty_set
        | ! [X4] : ~ in(X4,X3) )
      & ( ? [X5] : in(X5,X3)
        | X3 = empty_set ) ),
    inference(variable_rename,[status(thm)],[40]) ).

fof(42,plain,
    ! [X3] :
      ( ( X3 != empty_set
        | ! [X4] : ~ in(X4,X3) )
      & ( in(esk3_1(X3),X3)
        | X3 = empty_set ) ),
    inference(skolemize,[status(esa)],[41]) ).

fof(43,plain,
    ! [X3,X4] :
      ( ( ~ in(X4,X3)
        | X3 != empty_set )
      & ( in(esk3_1(X3),X3)
        | X3 = empty_set ) ),
    inference(shift_quantors,[status(thm)],[42]) ).

cnf(44,plain,
    ( X1 = empty_set
    | in(esk3_1(X1),X1) ),
    inference(split_conjunct,[status(thm)],[43]) ).

cnf(45,plain,
    ( X1 != empty_set
    | ~ in(X2,X1) ),
    inference(split_conjunct,[status(thm)],[43]) ).

fof(46,negated_conjecture,
    ? [X1,X2] :
      ( ( ~ disjoint(X1,X2)
        & ! [X3] : ~ in(X3,set_intersection2(X1,X2)) )
      | ( ? [X3] : in(X3,set_intersection2(X1,X2))
        & disjoint(X1,X2) ) ),
    inference(fof_nnf,[status(thm)],[17]) ).

fof(47,negated_conjecture,
    ? [X4,X5] :
      ( ( ~ disjoint(X4,X5)
        & ! [X6] : ~ in(X6,set_intersection2(X4,X5)) )
      | ( ? [X7] : in(X7,set_intersection2(X4,X5))
        & disjoint(X4,X5) ) ),
    inference(variable_rename,[status(thm)],[46]) ).

fof(48,negated_conjecture,
    ( ( ~ disjoint(esk4_0,esk5_0)
      & ! [X6] : ~ in(X6,set_intersection2(esk4_0,esk5_0)) )
    | ( in(esk6_0,set_intersection2(esk4_0,esk5_0))
      & disjoint(esk4_0,esk5_0) ) ),
    inference(skolemize,[status(esa)],[47]) ).

fof(49,negated_conjecture,
    ! [X6] :
      ( ( ~ in(X6,set_intersection2(esk4_0,esk5_0))
        & ~ disjoint(esk4_0,esk5_0) )
      | ( in(esk6_0,set_intersection2(esk4_0,esk5_0))
        & disjoint(esk4_0,esk5_0) ) ),
    inference(shift_quantors,[status(thm)],[48]) ).

fof(50,negated_conjecture,
    ! [X6] :
      ( ( in(esk6_0,set_intersection2(esk4_0,esk5_0))
        | ~ in(X6,set_intersection2(esk4_0,esk5_0)) )
      & ( disjoint(esk4_0,esk5_0)
        | ~ in(X6,set_intersection2(esk4_0,esk5_0)) )
      & ( in(esk6_0,set_intersection2(esk4_0,esk5_0))
        | ~ disjoint(esk4_0,esk5_0) )
      & ( disjoint(esk4_0,esk5_0)
        | ~ disjoint(esk4_0,esk5_0) ) ),
    inference(distribute,[status(thm)],[49]) ).

cnf(52,negated_conjecture,
    ( in(esk6_0,set_intersection2(esk4_0,esk5_0))
    | ~ disjoint(esk4_0,esk5_0) ),
    inference(split_conjunct,[status(thm)],[50]) ).

cnf(53,negated_conjecture,
    ( disjoint(esk4_0,esk5_0)
    | ~ in(X1,set_intersection2(esk4_0,esk5_0)) ),
    inference(split_conjunct,[status(thm)],[50]) ).

cnf(58,negated_conjecture,
    ( disjoint(esk4_0,esk5_0)
    | empty_set = set_intersection2(esk4_0,esk5_0) ),
    inference(spm,[status(thm)],[53,44,theory(equality)]) ).

cnf(70,negated_conjecture,
    disjoint(esk4_0,esk5_0),
    inference(csr,[status(thm)],[58,29]) ).

cnf(72,negated_conjecture,
    set_intersection2(esk4_0,esk5_0) = empty_set,
    inference(spm,[status(thm)],[30,70,theory(equality)]) ).

cnf(74,negated_conjecture,
    ( in(esk6_0,set_intersection2(esk4_0,esk5_0))
    | $false ),
    inference(rw,[status(thm)],[52,70,theory(equality)]) ).

cnf(75,negated_conjecture,
    in(esk6_0,set_intersection2(esk4_0,esk5_0)),
    inference(cn,[status(thm)],[74,theory(equality)]) ).

cnf(80,negated_conjecture,
    empty_set != set_intersection2(esk4_0,esk5_0),
    inference(spm,[status(thm)],[45,75,theory(equality)]) ).

cnf(83,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[72,80,theory(equality)]) ).

cnf(84,negated_conjecture,
    $false,
    83,
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SEU/SEU120+1.p
% --creating new selector for []
% -running prover on /tmp/tmpPjPwM1/sel_SEU120+1.p_1 with time limit 29
% -prover status Theorem
% Problem SEU120+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SEU/SEU120+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SEU/SEU120+1.p
% Solved 1 out of 1.
% # Problem is unsatisfiable (or provable), constructing proof object
% # SZS status Theorem
% # SZS output start CNFRefutation.
% See solution above
% # SZS output end CNFRefutation
% 
%------------------------------------------------------------------------------